# Sound problem

The size of your eardrum partially determines the upper frequency limit of your audible region, usually between 16,000 Hz and 20,000 Hz. If the wavelength is on the order of twice the diameter of the eardrum and the air temperature is 20 degrees Celcius, how wide is your eardrum?

I have no idea how to do this problem. I have looked at the equations for sound, but I don't whether there is an equation that can calculate width.

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Well, a look in my handy little book of physics formulas tells me that the speed of sound in an ideal gas is:

$$v = \left( \frac{\gamma R T}{\mu}\right)^{1/2}$$

where R is the molar gas constant, T is the temperature, $$\gamma$$ is the ratio of heat capacities and $$\mu$$ is the mean molecular mass. These are all quantities you should be able to find the values of by looking them up.

Now, wavelength is simply wave speed / frequency so you can now calculate the wavelength of the sound and hence estimate the width of the eardrum.

Hope that helps.

Matt